Adaptive artificial viscosity in calculations via non-uniform grids

The paper concerns with some adaptive artificial viscosity technique which is proposed for the numerical solution of gas-dynamic problems using non-uniform difference grids. The construction of a corresponding conservative difference scheme is developed for one-dimensional problem formulations. We’ve estimated the viscosity value bounds which give sufficient conditions for preserving a monotonicity property of the solution. The estimations take into acсount both the heterogeneity of gas-dynamic quantities (density, pressure, internal energy...) in the flow region, and the unevenness of the computational grid. Approbation of the modified methodology is carried out by calculating a number of well-known test problems. Computational experiments demonstrate a possibility of high-precision calculations via using grids incorporating adjacent computational cells with a great difference in sizes.